Momentum, Collisions and Explosions Legacy Problem #8 Guided Solution
Problem*
NASA's Langley Research Center has been experimenting with the use of air bags to soften the landings of crew exploration vehicles (CEV) on land. What stopping time will be required in order to safely stop a 7250 kg CEV moving at 7.65 m/s with an average force of 426000 N (an average force of 6 Gs)?
Audio Guided Solution
NASA has been experimenting for some time with the use of airbags on their crew exploration vehicles in an effort to lessen the amount of force that the occupants in the instrumentation experience when the crew exploration vehicles lands on land. In this question, we're looking at the collision between a vehicle whose mass is 7250 kg, moving at a speed of 7.65 m per second, and finally coming to a stop, 0 m per second, and encountering no more force than 426,000 newtons. This value for force happens to be equivalent to what we would term 6 g's of force, that is 6 times the actual weight of the occupants in the instrumentation, and we certainly would not want a whole lot more force than that. So the question here is, what is the stopping time? What time would be required in order to get this momentum to change by that amount with no more than that amount of force? We're going to use the Ft equals m delta v equation, the impulse equals momentum change equation. In this equation, we can solve for t by substituting in the value of force, 426,000 newtons, the value of mass, 7250 kg, and the velocity change to 7.65 m per second. You'll note in substituting the velocity change, I'm ignoring the negative side, because here we want to calculate time, and we're not concerned about a negative number. So as we do this calculation, we end up getting a value of 0.1302 seconds, and I can round that to three digits, and that's my answer.
Solution
0.130 seconds
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(m = 1.50 \unit{kg}\), \(v_i = 2.68 \unit{\meter\per\second}\), \(F = 4.98 \unit{\newton}\), \(t = 0.133 \unit{\second}\), \(v_f = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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